The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.

An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz / D.MUNDICI; R.CIGNOLI. - In: STUDIA LOGICA. - ISSN 0039-3215. - STAMPA. - 58:(1997), pp. 79-97. [10.1023/A:1004991931741]

An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz

MUNDICI, DANIELE;
1997

Abstract

The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.
1997
58
79
97
D.MUNDICI; R.CIGNOLI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/315189
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